Generalized Tensorial Simpson type Inequalities for Convex functions of Selfadjoint Operators in Hilbert Space

Year 2024, , 78 - 89, 08.11.2024

Vuk Stojiljkovic

https://doi.org/10.47087/mjm.1452521

Abstract

Several generalized Simpson tensorial type inequalities for self adjoint operators have been obtained with variation depending on the conditions imposed on the function f.

Keywords

Tensorial product, Selfadjoint operators, Convex functions

References

• [1] W. Afzal; M. Abbas; J.E. Macias-Dıaz; S. Treant, a. Some H-Godunova–Levin Function Inequalities Using Center Radius (Cr) Order Relation. Fractal Fract. 2022, 6, 518. https://doi.org/10.3390/fractalfract6090518
• [2] W.Afzal.;A.A.Lupas;K.Shabbir.Hermite–Hadamard and Jensen-Type Inequalities for Harmonical (h1, h2)-Godunova–Levin Interval-Valued Functions. Mathematics 2022, 10, 2970.https://doi.org/10.3390/math10162970
• [3] W.Afzal.,K. Shabbir, S.Treanta,K.Nonlaopon. Jensen and Hermite-Hadamard type inclusions for harmonical h-Godunova-Levin functions[J].Aims Mathematics, 2023, 8(2): 3303-3321.doi: 10.3934/math.2023170
• [4] W.Afzal.,K.Shabbir,T.Botmart.Generalized version of Jensen and Hermite-Hadamard inequalities for interval-valued (h1,h2)-Godunova-Levin functions[J].AIMSMathematics, 2022,7(10): 19372-19387.doi: 10.3934/math.20221064
• [5] W.Afzal,W.Nazeer,T.Botmart,S.Treanta. Some properties and inequalities for generalized class of harmonical Godunova-Levin function via center radius order relation[J]. AIMS Mathematics,2023,8(1): 1696-1712.doi: 10.3934/math.2023087
• [6] H. Araki and F. Hansen, Jensen´s operator inequality for functions of several variables, Proc. Amer. Math. Soc. 128 (2000), No. 7, 20
• [7] S.I Butt; M. Tariq; A. Aslam; H. Ahmad; T.A. Nofal. Hermite–Hadamard type inequalities via generalized harmonic exponential convexity and applications. J. Funct. Spaces 2021, 2021, 5533491.
• [8] S.I Butt, I. Javed, P. Agarwal et al. Newton–Simpson-type inequalities via majorization. J Inequal Appl 2023, 16 (2023). https://doi.org/10.1186/s13660-023-02918-0
• [9] A. Chandola , R. Agarwal , M. R. Pandey.Some New Hermite–Hadamard, Hermite–Hadamard Fejer and Weighted Hardy Type Inequalities Involving (k-p) Riemann Liouville Fractional Integral Operator, Appl. Math. Inf. Sci. 16, No. 2, 287–297 (2022).
• [10] H. Chen, U.N. Katugampola. Hermite–Hadamard and Hermite–Hadamard–Fejer type inequalities for generalized fractional integrals. J. Math. Anal. Appl. 2017, 446, 1274–1291
• [11] S.S. Dragomir. Applicable Analysis and Discrete Mathematics 2007 Volume 1, Issue 1, Pages: 92-110 https://doi.org/10.2298/AADM0701092D
• [12] S.S. Dragomir, The Hermite-Hadamard type Inequalities for Operator Convex Functions, Applied Mathematics and Computation Volume 218, Issue 3, 1 October 2011, Pages 766-772
• [13] S.S Dragomir, Tensorial Norm Inequalities For Taylor’s Expansions Of Functions Of Selfadjoint Operators In Hilbert Spaces , ResearchGate, November 2022.
• [14] S.S Dragomir, An Ostrowski Type Tensorial Norm Inequality For Continuous Functions Of Selfadjoint Operators In Hilbert Spaces, Researchgate, November 2022.
• [15] S.S. Dragomir, C.E.M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, in: RGMIA Monographs, Victoria University, 2000.
• [16] S.S. Dragomir. A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces. Istanbul Journal of Mathematics. 2023;1(2):48-56. https://doi.org/10.26650/ijmath.2023.00006
• [17] S.S. Dragomir. Gradient Inequalities for an Integral Transform of Positive Operators in Hilbert Spaces, Annales Mathematicae Silesianae Volume 37 (2023): Issue 2 (September 2023), https://doi.org/10.2478/amsil-2023-0008
• [18] H. Guo, What Are Tensors Exactly?, World Scientific, June 2021, https://doi.org/10.1142/12388
• [19] F. Hezenci, H. Budak, H. Kara. New version of fractional Simpson type inequalities for twice differentiable functions. Adv. Differ. Equ. 2021, 460 (2021). https://doi.org/10.1186/s13662 021-03615-2
• [20] A. Koranyi. On some classes of analytic functions of several variables. Trans. Amer. Math. Soc., 101 (1961), 520-554.
• [21] D. S. Mitrinovi´c ,Analytic Inequalities, Springer-Verlag, Berlin, 1970.
• [22] J., Nasir, S., Qaisar, S. I., Butt, A. K., Khan, R. S., Mabela, Some Simpson’s Riemann–Liouville Fractional Integral Inequalities with Applications to Special Functions, Journal of Function Spaces, 2022, 2113742, 12 pages, 2022. https://doi.org/10.1155/2022/2113742
• [23] J. Peˇcari´c , F. Proschan , Y. Tong , Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, INC, United States of America, 1992.
• [24] T. Rasheed, S. I. Butt, G. Peˇcari´c, and ¯D. Peˇcari´ c, New bounds of Popoviciu’s difference via weighted Hadamard type inequalities with applications in information theory, Math. Meth. Appl. Sci. 47 (2024), 5750–5763, DOI 10.1002/mma.9889.
• [25] T. Rasheed, S.I. Butt, ¯D. Peˇcari´c, J. Peˇcari´c, Generalized cyclic Jensen and information inequalities, Chaos, Solitons & Fractals, Volume 163, 2022, 112602, ISSN 0960-0779, https://doi.org/10.1016/j.chaos.2022.112602.
• [26] M.Z. Sarikaya, E. Set, M.E. Ozdemir, On new inequalities of Simpson’s type for convex functions, RGMIA Res. Rep. Coll. 13 (2) (2010) Article2.
• [27] M. Z. Sarıkaya and S. Bardak, “Generalized Simpson Type Integral Inequalities”, Konuralp J. Math., vol. 7, no. 1, pp. 186–191, 2019.
• [28] V. Stojiljkovic, Simpson Type Tensorial Norm Inequalities for Continuous Functions of ´ Selfadjoint Operators in Hilbert Spaces, Creat. Math. Inform., 33 (2024), 105–117. https://doi.org/10.37193/CMI.2024.01.10
• [29] V. Stojiljkovi´ c; R. Ramaswamy; O.A.A. Abdelnaby; S. Radenovi´c. Some Refine ments of the Tensorial Inequalities in Hilbert Spaces. Symmetry 2023, 15, 925. https://doi.org/10.3390/sym15040925
• [30] V. Stojiljkovi´c.; Hermite–Hadamard–type fractional–integral inequalities for (p,h) convex fuzzy-interval-valued mappings, Electron. J. Math. 5 (2023) 18–28, DOI: 10.47443/ejm.2023.004
• [31] V. Stojiljkovi´ c. (2023). ’Twice Differentiable Ostrowski Type Tensorial Norm Inequal ity for Continuous Functions of Selfadjoint Operators in Hilbert Spaces’ , Electronic Journal of Mathematical Analysis and Applications, 11(2), pp. 1-15. doi: 10.21608/ej maa.2023.199881.1014
• [32] V. Stojiljkovi´c. Twice Differentiable Ostrowski Type Tensorial Norm Inequality for Contin uous Functions of Selfadjoint Operators in Hilbert Spaces. European Journal of Pure and Applied Mathematics, 16(3), (2023), 1421–1433.
• [33] V. Stojiljkovi´ c., & S.S. Dragomir. (2023). Differentiable Ostrowski type tensorial norm in equality for continuous functions of selfadjoint operators in Hilbert spaces. Gulf Journal of Mathematics, 15(2), 40-55. https://doi.org/10.56947/gjom.v15i2.1247
• [34] V. Stojiljkovi´c; N. Mirkov; S. Radenovi´c. Variations in the Tensorial Trapezoid Type Inequal ities for Convex Functions of Self-Adjoint Operators in Hilbert Spaces. Symmetry 2024, 16, 121. https://doi.org/10.3390/sym16010121